Signed curvature of a plane graph ($\kappa =\frac{u_{xx}}{(1+u_x^2{)}^{3/2}}$)

For an oriented plane curve written locally as the graph $(x,u(x))$, its signed curvature isThe equation $\kappa =0$ describes straight lines, while $\kappa =1/R$ describes consistently oriented arcs of circles of radius $R$.